We propose a general framework to analyse how vulnerable to manipulation social choice functions are when a limited amount of information about individual preferences is available. We focus then on two properties called WMG-strategy-proofness and group WMG-strategy-proofness. A social choice function is [group] WMG-strategy-proof if it cannot be manipulated by an individual [a coalition of individuals] whose information about the preferences of the others is limited to the knowledge, for every pair of alternatives, of the number of people preferring the first alternative to the second one. We prove that there are Pareto optimal, WMG-strategy-proof and non-dictatorial social choice functions, that every Pareto optimal and WMG-strategy-proof social choice function is not anonymous if the alternatives are at least three, and that every Pareto optimal and group WMG-strategy-proof social choice function is dictatorial if the alternatives are three.

我们提出了一个通用框架来分析当关于个人偏好的信息量有限时，社会选择函数对操纵的脆弱性。然后我们关注两个属性，称为 WMG-strategy-proofness 和 group WMG-strategy-proofness。如果一个社会选择函数不能被个人 [个人联盟] 操纵，则该函数是 [群体] WMG 策略证明的，该个人[个人联盟] 的信息仅限于对每对选项的数量的了解的人更喜欢第一个选择而不是第二个。我们证明存在帕累托最优、WMG 策略证明和非独裁社会选择函数，如果备选方案至少为三个，则每个帕累托最优和 WMG 策略证明社会选择函数都不是匿名的，